Suppose we have two functions: \( f(x)=x^{2}+1 \) and \( g(x)=3 x+5 \). Find the value of \( f(-1) g(-1) \). 4 16 11

To find the value of \( f(-1) g(-1) \), we first need to compute \( f(-1) \) and \( g(-1) \). Starting with \( f(-1) \): \[ f(-1) = (-1)^2 + 1 = 1 + 1 = 2 \] Now, for \( g(-1) \): \[ g(-1) = 3(-1) + 5 = -3 + 5 = 2 \] Next, we multiply these results: \[ f(-1)g(-1) = 2 \cdot 2 = 4 \] So, the value of \( f(-1) g(-1) \) is \( 4 \). To connect these functions to the world of mathematics, polynomial functions like \( f(x) \) are foundational in algebra. They model a plethora of real-world phenomena, such as projectile motion or business profit models. Understanding how to manipulate and evaluate them is crucial for more advanced topics like calculus. If you're curious about enhancing your mathematical journey, consider delving into topics like function transformations and their graphical representations. Books and online platforms often provide engaging ways to see these concepts in action, making learning both fun and impactful!